Average Error: 6.1 → 1.0
Time: 31.8s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\left(\frac{\sqrt[3]{y}}{\sqrt[3]{a}} \cdot \left(z - t\right)\right) \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{a} \cdot \sqrt[3]{a}} + x\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\left(\frac{\sqrt[3]{y}}{\sqrt[3]{a}} \cdot \left(z - t\right)\right) \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{a} \cdot \sqrt[3]{a}} + x
double f(double x, double y, double z, double t, double a) {
        double r14499720 = x;
        double r14499721 = y;
        double r14499722 = z;
        double r14499723 = t;
        double r14499724 = r14499722 - r14499723;
        double r14499725 = r14499721 * r14499724;
        double r14499726 = a;
        double r14499727 = r14499725 / r14499726;
        double r14499728 = r14499720 + r14499727;
        return r14499728;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r14499729 = y;
        double r14499730 = cbrt(r14499729);
        double r14499731 = a;
        double r14499732 = cbrt(r14499731);
        double r14499733 = r14499730 / r14499732;
        double r14499734 = z;
        double r14499735 = t;
        double r14499736 = r14499734 - r14499735;
        double r14499737 = r14499733 * r14499736;
        double r14499738 = r14499730 * r14499730;
        double r14499739 = r14499732 * r14499732;
        double r14499740 = r14499738 / r14499739;
        double r14499741 = r14499737 * r14499740;
        double r14499742 = x;
        double r14499743 = r14499741 + r14499742;
        return r14499743;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original6.1
Target0.6
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;y \lt -1.0761266216389975 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Initial program 6.1

    \[x + \frac{y \cdot \left(z - t\right)}{a}\]

  2. Simplified2.5

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, z - t, x\right)}\]
  3. Using strategy rm

  4. Applied fma-udef2.5

    \[\leadsto \color{blue}{\frac{y}{a} \cdot \left(z - t\right) + x}\]
  5. Using strategy rm

  6. Applied add-cube-cbrt3.0

    \[\leadsto \frac{y}{\color{blue}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}}} \cdot \left(z - t\right) + x\]

  7. Applied add-cube-cbrt3.1

    \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}} \cdot \left(z - t\right) + x\]

  8. Applied times-frac3.1

    \[\leadsto \color{blue}{\left(\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{a}}\right)} \cdot \left(z - t\right) + x\]

  9. Applied associate-*l*1.0

    \[\leadsto \color{blue}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \left(\frac{\sqrt[3]{y}}{\sqrt[3]{a}} \cdot \left(z - t\right)\right)} + x\]

  10. Final simplification1.0

    \[\leadsto \left(\frac{\sqrt[3]{y}}{\sqrt[3]{a}} \cdot \left(z - t\right)\right) \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{a} \cdot \sqrt[3]{a}} + x\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"

  :herbie-target
  (if (< y -1.0761266216389975e-10) (+ x (/ 1 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (+ x (/ (* y (- z t)) a)) (+ x (/ y (/ a (- z t))))))

  (+ x (/ (* y (- z t)) a)))